A new methodology to effectively forecast fire dynamics based on assimilation of sensor observations is presented and demonstrated. An inverse modelling approach with a two-zone model is used to forecast the growth of a compartment fire. Sensor observations are assimilated into the model in order to estimate invariant parameters and thus speed up simulations and recover information lost by modelling approximations. A series of cases of a compartment fire radially spreading at different growth rates (slow, medium and fast) are used to test the methodology. Spread rate, entrainment coefficient and smoke transport time are the invariant parameters estimated via a gradient-based optimization method with tangent linear differentiation. The parameters were estimated accurately within minutes after ignition and the heat release rate reproduced satisfactorily in all cases. Moreover, the temperature and the height of the hot layer are forecasted with a positive lead time between 50 and 80 s, depending on the fire growth rate. The results show that the simple mass and energy conservation equations and plume correlation of the zone model are suitable to forecast the main features of a growing fire. Positive lead times are reported here for the first time in fire dynamics. The results also suggest the existence of an optimal width for the assimilation window. The proposed methodology is subject to ongoing research and the results are an important step towards the forecast of fire dynamics to lead the emergency response.